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Simplifying ln(3x) + ln(3) = ln(7x + 2) Remove parenthesis around (3x) ln * 3x + ln(3) = ln(7x + 2) Reorder the terms for easier multiplication: 3ln * x + ln(3) = ln(7x + 2) Multiply ln * x 3lnx + ln(3) = ln(7x + 2) Reorder the terms for easier multiplication: 3lnx + 3ln = ln(7x + 2) Reorder the terms: 3ln + 3lnx = ln(7x + 2) Reorder the terms: 3ln + 3lnx = ln(2 + 7x) 3ln + 3lnx = (2 * ln + 7x * ln) 3ln + 3lnx = (2ln + 7lnx) Solving 3ln + 3lnx = 2ln + 7lnx Solving for variable 'l'. Move all terms containing l to the left, all other terms to the right. Add '-2ln' to each side of the equation. 3ln + -2ln + 3lnx = 2ln + -2ln + 7lnx Combine like terms: 3ln + -2ln = 1ln 1ln + 3lnx = 2ln + -2ln + 7lnx Combine like terms: 2ln + -2ln = 0 1ln + 3lnx = 0 + 7lnx 1ln + 3lnx = 7lnx Add '-7lnx' to each side of the equation. 1ln + 3lnx + -7lnx = 7lnx + -7lnx Combine like terms: 3lnx + -7lnx = -4lnx 1ln + -4lnx = 7lnx + -7lnx Combine like terms: 7lnx + -7lnx = 0 1ln + -4lnx = 0 Factor out the Greatest Common Factor (GCF), 'ln'. ln(1 + -4x) = 0Subproblem 1
Set the factor 'ln' equal to zero and attempt to solve: Simplifying ln = 0 Solving ln = 0 Move all terms containing l to the left, all other terms to the right. Simplifying ln = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + -4x)' equal to zero and attempt to solve: Simplifying 1 + -4x = 0 Solving 1 + -4x = 0 Move all terms containing l to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = 0 + -1 -4x = 0 + -1 Combine like terms: 0 + -1 = -1 -4x = -1 Add '4x' to each side of the equation. -4x + 4x = -1 + 4x Combine like terms: -4x + 4x = 0 0 = -1 + 4x Simplifying 0 = -1 + 4x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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